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Models of ad-hoc wireless networks are often based on the geometric disc abstraction: transmission is assumed to be isotropic, and reliable communication channels are assumed to exist (apart from interference) between nodes closer than a given distance. In reality communication channels are unreliable and communication range is generally not rotationally symmetric. This paper examines how these issues affect network connectivity. Using ideas from percolation theory, they compare networks of geometric discs to other simple shapes, including probabilistic connections, and they find that when transmission range and node density are normalized across experiments so as to preserve the Expected Number of Connections (ENC) enjoyed by each node, the discs are the "Hardest" shape to connect together.
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